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Shielding Theory (A Critical Look)
By George M. Kunkel
Introduction
During the late 60s and early 70s, I taught courses on EMC
system design at the Extension Department of UCLA. One of
the subjects covered was Shielding of EM Waves. The theory
which was taught is consistent with the theory contained in
the book by Ott. One of my students (who had a PhD degree
in Physics from MIT) took exception to the theory. His comments
were that the impedance of the barrier assumes an infinitely
thick barrier where the thickness of the barriers on his spacecraft
are of finite thickness, and absorption loss is an I2R loss,
not skin effect. This paper will examine these comments and
other comments which I encountered during my 17 years as chairman
of the Technical Committee on Interference Control of the
EMC Society of the IEEE.
Shielding Critique
Shielding theory stipulates that there is a reflection loss
“R”, absorption loss “A” and a re-reflection
coefficient “B” and that the energy in the wave
emanating from the transmitted side of the barrier is equal
to the energy striking the barrier minus the losses as a result
of: (1) the reflection loss at the incident side of the barrier,
(2) loss at the transmitted side of the barrier, and (3) the
losses inside the barrier. The theory also stipulates that
there is a re-reflection coefficient that exists when the
barrier is less than the extension depth of the wave (i.e.,
when the thickness of the shielding barrier is less than 2P times
the skin depth). The paragraphs that follow evaluate the shielding
theory as presented by Ott. (Ott is used because the shielding
theory presented in his book is the theory which is accepted
by the EMC Society of the IEEE.)
Reflection Loss
The reflection loss as utilized in shielding theory is obtained
directly from our textbooks on electromagnetic theory. However,
the boundary conditions are not consistent with the boundary
conditions used in the textbooks. The accepted equation of
the reflection loss “R” is:
The boundary condition stipulated in the text books is that
the thickness of the barrier is at least an extension depth
or 2Pd In shielding theory there is no boundary condition
(i.e., the impedance of the barrier is consistent irrespective
of the thickness of the barrier). It can be shown that the
actual impedance of the barrier varies significantly with
the thickness of the barrier when the thickness is less than
the extension depth. The equation for the impedance of the
barrier can be obtained by integrating the thickness with
respect to skin effect. That is, the normalized conductive
area of a barrier is equal to:
for all thickness of a barrier. This yields an impedance
of a barrier as follows:
As an example, we know from the ITT handbook that the area
of a #10 copper wire conductor is 5.26 x 10-6 meters
squared and it has a resistance of 3.27 x 10-3 ohms
per meter length. If we take the wire and flatten it out to
be a sheet one meter wide, the thickness would be 5.26 x
10-6 meters. The resistance would remain the same or 3.27
x 10-3 ohms per meter length. This can be verified by
using the equation for the resistance of a metal sheet of
equal length and width, i.e.,
The contents of the table below illustrate the significant
difference in the value of the impedance as a function of
the frequency of a wave striking the barrier and the Equations
4 and 6.
It is interesting to note that the thickness of the barrier
is much less than the skin depth (as is the case for the frequency
at 1kHz) the resistance associated with the impedance of ZB4
and ZB6 is the same as the resistance of the wire, i.e.,
It can also be noted that when the thickness is greater than
the extension depth, the impedance is the same for
ZB4 and ZB6 (as in the case for the frequency at 10GHz).
This difference in the impedance of the barrier means that
there must be a correction factor to correct for the actual
impedance when the thickness of the barrier is less than the
extension depth. It is interesting to note that the value
of the difference in the impedance between ZB4 and ZB6 is
approximately equal to the value of the re-reflection coefficient
“B” as defined by Ott, i.e.,
Absorption Loss
Ott, as well as all other books and papers on shielding,
describe the skin effect as an absorption loss, i.e.,
We learn from high school physics classes that power (absorption
) loss is an I2R factor. Hallen tells us that the power (absorption)
loss in a shielding barrier when the barrier is thicker than
an extension depth is as follows:
The term “absorption less” used in the EMC community
as illustrated by Ott is really an attenuating factor caused
by skin effect, not as an absorption or power loss.
Re-Reflection Coefficient
Shielding theory as described by Ott states that there is
a reflection loss at the incident side of a shielded barrier
and another at the transmitting side. At the incident side,
the E field is reflected (the H field actually doubles). At
the transmitting side the H field is reflected, where the
impedance of the transmitted wave which leaves the barrier
is identical to the impedance of the incident wave which strikes
the barrier. This is implied to be true irrespective of the
impedance of the wave. This means that if you have a pair
of wires as illustrated in Figure 1 on page 18. If the transmission
line is carrying a 20kHz signal, the impedance of the wave
leaving the barriers will be approximately 1.8 x 106
ohms, i.e
The wave emanating from the pair of wires approximates that
of an electric dipole antenna. The impedance of a wave as
a function of distance from an electric dipole antenna is
approximated by Equation 9:
If the pair of wires is replaced by a transformer which
is carrying 20kHz current, the impedance of the wave emanating
from the barrier is approximately 0.8 ohms, i.e.,
The wave emanating from a transformer approximates that of
a magnetic dipole antenna. The impedance of a wave as a function
of distance from a magnetic dipole antenna is approximated
by:
This requires an intelligence of the electrons in a shielding
barrier that is hard to accept, i.e.,
Hallen tells us that the impedance of the wave in the barrier
is equal to the impedance of the barrier. He also tells us
that the surface current density “Js” is equal to
the H field; therefore the E field is equal to the H field
times the impedance of the barrier. What the shielding theory
tells us is that the relative magnitude of the H reflected
field at the transmitted secondary side is a function of the
impedance of the wave at the incident side. It is difficult
to accept that the electrons (represented by the surface current
density Js) as they move through the barrier have the capability
of remembering what the impedance of the forcing (or incident)
field is and reacting at the secondary side in a relationship
which is equal to the impedance of the wave at the incident
side (i.e., the relative magnitude of the H field emanating
from the transmitted side of the barrier is a function of
the impedance of the incident wave).
EM Shielding Using Circuit Theory
The undergraduate courses on electromagnetic theory introduce
the concept of an electromagnetic wave by driving a pair of
parallel plates with an AC voltage source as illustrated in
Figure 2.
As illustrated, a displacement field (displacement current)
is generated between the plates. At the edge of the plates
the lines of force bow out creating an EM field. If a shielding
barrier is placed in the path of the lines of force of the
field, the lines of force will cause a current Js to flow
in the barrier as illustrated in Figure 3.
We know from Hallen that the magnitude of Js will be approximately
equal to twice the value of the H field of the incident wave
at the barrier. The current Js will create E and H fields
inside the barrier. The E field is parallel to the flow of
the current and equal to JSZB. The H field is at right angles
to the current flow and equal in magnitude. The H field will
generate a back emf forcing the magnitude of the current in
the barrier to decrease with depth where the incremental amplitude
of Js varies as illustrated in Figure 4. Since the E and H
fields vary directly proportionally to Js, the incremental
E and H fields will decrease with depth. The current in the
barrier on the secondary side of the barrier will be equal
to “Js” attenuated by skin effect, i.e.,
The values of the E and H vector fields at the transmitted
side will also be equal to the E and H fields at the incident
side of the barrer as attenuated by skin effect, i.e.,
The current Js will generate a field on the transmitted
side, where it is hypothesized that the filed will be equal
to Et and Ht.
Note: Shielding theory as described by Ott tells us that
the current Js (i.e., the H field) will be reflected at the
transmitted side of the barrier where the reflection coefficient
will be equal to the E field reflection coefficient at the
incident side. We are also told that the magnitude of the
E field emanating from the barrier on the secondary side is
equal to that obtained using Equation 12 or 14. It is very
difficult to accept the theory that the current Js and H field
is reduced without an equal reduction in the E field (i.e.,
E = HZB). It is also difficult to accept the reduction of
the current without an outside force being exerted on the
shield.
Summary
We are told that the theory on the shielding of electromagnetic
waves is derived directly from our textbooks on EM theory.
However, significant anomalies exist between the contents
of the information in our textbooks and the information presented
in our shielding theory. These anomalies are as follows:
1. In the development of the reflection coefficient our
textbooks stipulate two boundary conditions which are not
observed in our shielding theory. These are:
a) The thickness of a barrier is equal to an extension depth
or greater.
b) Impedance of the incident wave is equal to 377ohms.
2. Absorption (or power) loss in our textbooks is defined
as an I2R loss. Shielding theory defines skin effect as an
absorption loss.
3. Shielding theory as described by Ott tells us that the
reflection coefficient at the transmitting side of the barrier
is an H field reflection coefficient (i.e., at the incident
side of the barrier the E field is reflected and at the secondary
or transmitted side the H field is reflected. This yields
an equal magnitude of reflected E and H fields by the barrier).
Our textbooks (i.e., Hallen) inform us that the value of E
in the barrier is equal to H ZB . This means that when the
H field in the barrier is reduced due to the reflection at
the secondary side, the E field is reduced proportionally.
4. Shielding theory as presented by Ott informs us that
the wave takes on the impedance of the barrier upon entering
the barrier and that the impedance of the barrier is constant
irrespective of the thickness of the barrier (i.e., the impedance
of the barrier is not reduced as a function of the thickness
of the barrier when the thickness of the barrier is less than
the extension depth). This implies that the impedance of a
barrier as seen by the wave can be as much as two or three
orders of magnitude less than the resistance of the barrier
as measured by a resistance bridge.
Conclusion
The electrical/electronic design engineering community views
the EMC discipline as a black magic art. This to a large degree
is due to the fact that the EMC engineers use: (1) different
logic in solving problems; (2) different equation s to explain
their logic; and (3) a different vocabulary than the rest
of the scientific community. The anomalies listed in this
paper illustrate some of the problems inherent in the communication
problems between the EMC engineer and the scientific community.
It is strongly recommended that the EMC engineering community
evaluate the theory, equations and vocabulary used within
the EMC discipline. The purpose would be to better communicate
with the rest of the technical community. The result would
place the EMC discipline on a much stronger technical plane
and provide young graduate engineers an opportunity to enter
the exiting and complex EMC design engineering discipline
directly from college. They could then directly apply the
information contained in their engineering courses to solve
their EMC problems.
References
[1] Hallen, Erik, Electromagnetic Theory, John Wiley &
Sons Inc., New York, 1962.
[2] Hayt, William H., Engineering Electromagnetics, McGraw-Hill
Book Co., New York, 1958.
[3] Hershberger, “Introduction to Electromagnetic Theory”,
Class notes, ENGR 117 A/B UCLA, 1961.
[4] I.T.T, Reference Data for Radio Engineers, Stanford Press,
Inc., New York, 1956.
[5] Kunkel, George M., “Design of Transfer Impedance
Test Fixture Accurate Through 10GHz,” IEEE 1990 International
Symposium on EMC, Washington DC, August 1990.
[6] Ott, Henry W., Noise Reduction Techniques in Electronic
Systems, John Wiley & Sons, New York, 1976.
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